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Tuesday, December 31, 2013

As the year nears its end, my feed is full with last year’s news. For balance, I want to give some space to next year’s news. What do you think will be in the news next year?

In the very short run, technological developments aren’t so difficult to foresee, mostly because our brains all tick similarly. But by the time I have an idea, it’s highly likely somebody is already working on it. I’m not much of an inventor.

After the babies were born for example I remarked to Stefan that it’s about time somebody comes up with a high-tech diaper that sends me an email if full. Done.

Here are three of my speculations that I haven’t yet heard much about:

Robotic brain extension

Insects’ brains can hooked up to chips and be remote controlled. But rather than using a computer to control a biological neural network, it would be much cooler if one could integrate the bio-brain to improve the tasks that robots are typically bad at. Balance for example is such a case that is extremely difficult for robots, yet the smallest bird-brain can easily balance a body on one leg, thanks to million of years of evolution. Can one engineer the both to work together, provided some ethics committee nods approval?

Inaudibility shield

Forget about invisibility shields, nobody wants to be invisible, just look at youtube. What we really need in the days of iPhones and people talking to their glasses is an inaudibility shield. I neither want to hear your phone calls, nor do you want to hear mine. Somebody please work on this.

The conscious subconsciousness

I read all the time about computers that are brain-controlled or most recently brain to brain communication. However, the former is still far too cumbersome and will remain so for a long time, and the latter creeps out most people. So let’s stick with one head and just route signals from the unconscious parts of our brain activity to the conscious parts and vice versa. Imagine for a moment how dramatically the world might change if we had the ability to readjust hormonal balance or heart rate.

Friday, December 27, 2013

The kids are almost three years now and I spend a lot of time picking up wooden building blocks. That’s good for your health in many ways, for example by the following brain gymnastics.

When I scan the floor under the couch for that missing cube, I don’t expect to find it balancing on a corner - would you? And in the strange event that you found it delicately balanced on a corner, would you not expect to also find something, or somebody, that explains this?

When physicists scanned the LHC data for that particle, that particle you’re not supposed to call the god-particle, they knew it would be balancing on a corner. The Higgs is too light, much too light, that much we knew already. And so, before the LHC most physicists expected that once they’d be able to see the Higgs, they’d also catch a glimpse of whatever it was that explained this delicate balance. But they didn’t.

It goes under the name ‘naturalness,’ the belief that a finely tuned balance requires additional explanation. “Naturally” is the physicist’s way of saying “of course”. Supersymmetry, neatified to Susy, was supposed to be the explanation for finetuning, but Susy has not shown up, and neither has anything else. The cube stands balanced on the corner, seemingly all by itself.

Of course those who built their career on Susy cross-sections are not happy. They are now about to discard naturalness, for this would mean Susy could hide everywhere or nowhere, as long as it’s not within reach of the LHC. And beyond the LHC there’s 16 orders of magnitude space for more papers. Peter Woit tells this tale of changing minds on his blog. The denial of pre-LHC arguments is so bold it deserves a book (hint, hint), but that’s a people-story and not mine to tell. Let me thus leave aside the psychological morass and the mud-throwing, and just look at the issue at hand: Naturalness, or its absence respectively.

I don’t believe in naturalness, the idea that finetuned parameter values require additional explanation. I recognize that it can be a useful guiding principle, and that apparent finetuning deserves a search for its cause, but it’s a suggestion rather than a requirement.

I don’t believe in naturalness because the definition of finetuning itself is unnatural in its focus on numerical parameters. The reason physicists focus on numbers is that numbers are easy to quantify - they are already quantified. The cosmological constant is 120 orders of magnitude too large, which is bad with countably many zeros. But the theories that we use are finetuned to describe our universe in many other ways. It’s just that physicists tend to forget how weird mathematics can be.

We work with manifolds of integer dimension that allow for a metric and a causal structure, we work with smooth and differentiable functions, we work with bounded Hamiltonians and hermitian operators and our fibre bundles are principal bundles. There is absolutely no reason why this has to be, other than that evidence shows it describes nature. That’s the difference between math and physics: In physics you take that part of math that is useful to explain what you observe.
Differentiable functions, to pick my favorite example because it can be quantified, have measure zero in the space of all functions. That’s infinite finetuning. It’s just that nobody ever talks about it. Be wary whenever you meet the phrase “of course” in a scientific publication – infinity might hide behind it.

This finetuning of mathematical requirements appears in form of axioms of the theory – it’s a finetuning in theory space, and a selection is made based on evidence: differentiable manifolds with Lorentzian metric and hermitian operators work. But selecting the value of numerical parameters based on observational evidence is no different from selecting any other axiom. The existence of ‘multiverses’ in various areas of physics is similarly a consequence of the need to select axioms. Mathematical consistency is simply insufficient as a requirement to describe nature. Whenever you push your theory too far and ties to observation loosen too much, you get a multiverse.

My disbelief in naturalness used to be a fringe opinion and it’s gotten me funny looks on more than one occasion. But the world refused to be as particle physicists expected, naturalness rapidly loses popularity, and now it’s my turn to practice funny looks. The cube, it’s balancing on a tip and nobody knows why. In desparation they throw up their hands and say “anthropic principle”. Then they continue to produce scatter plots. But it’s a logical fallacy called ‘false dichotomy’, the claim that if it’s not natural it must be anthropic.

That I don’t believe in naturalness as a requirement doesn’t mean I think it a useless principle. If you have finetuned parameters, it will generally be fruitful to figure out the mechanism of finetuning. This mechanism will inevitably constitute another incidence of finetuning in one way or the other, either in parameter space or in theory space. But along the line you can learn something, while falling back on the anthropic principle doesn’t teach us anything. (In fact, we alreadyknow itdoesn’t work.) So if you encounter finetuning, it’s a good idea to look for a mechanism. But don’t expect that mechanism to work without finetuning itself - because it won’t.

If that was too many words, watch this video:

It’s a cube that balances on a tip. If your resolution scale is the size of the cube, all you will find is that it’s mysteriously finetuned. The explanation for that finetuned balance you can only find if you look into the details, on scales much below the size of the cube. If you do, you’ll find an elaborate mechanism that keeps the cube balanced. So now you have an explanation for the balance. But that mechanism is finetuned itself, and you’ll wonder then just why that mechanism was there in the first place. That’s the finetuning in theory space.

Now in the example with the above video we know where the mechanism originated. Metaphors all have their shortcomings, so please don’t mistake me for advocating intelligent design. Let me just say that the origin of the mechanism was a complex multi-scale phenomenon that you’d not be able to extract in an effective field theory approach. In a similar way, it seems plausible to me that the unexplained values of parameters in the standard model can’t be derived from any UV completion by way of an effective field theory, at least not without finetuning. The often used example is that hundreds of years ago it was believed that the orbits of planets have to be explained by some fundamental principles (regular polygons stacked inside each other, etc). Today nobody would assign these numbers fundamental relevance.

Of course I didn’t find a cube balancing on a tip under the couch. I didn’t find the cube until I stepped on it the next morning. I did however quite literally find a missing puzzle piece – and that’s as much as a theoretical physicist can ask for.

Tuesday, December 24, 2013

The next days will be a slow time on the blog as we're working our way through the holidays, the kid's 3rd birthday, and new year, with all the family and friend's visits that come with it. Back to business next year - enjoy the silence :)

Thursday, December 19, 2013

Whether or not space and time are fundamentally discrete is one of the central questions of quantum gravity. Discretization is a powerful method to tame divergences that plague the quantization of gravity, and it is thus not surprising that many approaches to quantum gravity rely on some discrete structure, may that be condensed matter analogies, triangulations, or approaches based on networks. One expects that discretization explains the occurrence of singularities in general relativity as unphysical, much like singularities in hydrodynamics are merely mathematical artifacts that appear because on short distances the fluid approximation for collections of atoms is no longer applicable.

But finding experimental evidence for space-time discreteness is difficult because this structure is at the Planck scale and thus way beyond what we can directly probe. The best tests for such discrete approaches thus do not rely on the discreteness itself but on the baggage it brings, such as violations or deformations of Lorentz-symmetry that can be very precisely tested. Alas, what if the discrete structure does not violate Lorentz-symmetry? That is the question I have addressed in my two recentpapers.

In discrete approaches to quantum gravity, space-time is not, fundamentally, a smooth background. Instead, the smooth background that we use in general relativity – the rubber sheet on which the marbles roll – is only an approximation that becomes useful at long distances. The discrete structure itself may be hard to test, but in any such discrete approach one expects the approximation of the smooth background to be imperfect. The discrete structure will have defects, much like crystals have defects, just because perfection would require additional explanation.

The presence of space-time defects affects how particles travel through the background, and the defects thus become potentially observable, constituting indirect evidence for space-time discreteness.To be able to quantify the effects, one needs a phenomenological model that connects the number and type of defects to observables, and can in return serve to derive constraints on the prevalence and properties of the defects.

In my papers, I distinguished two different types of defects: local defects and non-local defects. The requirement that Lorentz-invariance is maintained (on the average) turned out to be very restrictive on what these defects can possibly do.

The local defects are similar to defects in crystals, except that they are localized both in space and in time. These local defects essentially induce a violation of momentum conservation. This leads to a fairly straight-forward modification of particle interactions whenever a defect is encountered that makes the defects potentially observable even if they are very sparse.

The non-local defects are less intuitive from the particle-physics point of view. They were motivated by what Markopoulou and Smolin called ‘disordered locality’ in spin-networks, just that I did not, try as I might, succeed in constructing a version of disordered locality compatible with Lorentz-invariance. The non-local defects in my paper are thus essentially the dual of the local defects, which renders them Lorentz-invariant (on the average). Non-local defects induce a shift in position space in the same way that the local defects induce a shift in momentum space.

I looked at a bunch of observable effects that the presence of defects of either type would lead to, such as CMB heating (from photon decay induced by scattering on the local defects) or the blurring of distant astrophysical sources (from deviations of photons from the lightcone caused by non-local defects). It turns out that generally the constraints are stronger for low-energetic particles, in constrast to what one finds in deformations of Lorentz-invariance.

Existing data give some pretty good constraints on the density of defects and the parameters that quantify the scattering process. In the case of local defects, the density is roughly speaking less than one per fm4. That’s an exponent, not a footnote: It has to be a four-volume, otherwise it wouldn’t be Lorentz-invariant. For the non-local defects the constraints cannot as easily be summarized in a single number because they depend on several parameters, but there are contour plots in my papers.

The constraints so far are interesting, but not overwhelmingly exciting. The reason is that the models are only for flat space and thus not suitable to study cosmological data. To make progress, I'll have to generalize them to curved backgrounds. I also would like to combine both types of defects in a single model. I am presently quite excited about this because there is basically nobody who has previously looked at space-time defects, and there’s thus a real possibility that analyzing the data the right way might reveal something unexpected. And into the other direction, I am looking into a way to connect this phenomenological model to approaches to quantum gravity by extracting the parameters that I have used. So, you see, more work to do...

Sunday, December 15, 2013

“I was always bad at math” is an excuse I have heard many of my colleagues complain about. I’m reluctant to join their complaints. I’ve been living in Sweden for four years now and still don’t speak Swedish. If somebody asks me, I’ll say I was always bad with languages. So who am I to judge people for not wanting to make an effort with math?

People don’t learn math for the same reason I haven’t learned Swedish: They don’t need it. It’s a fact that my complaining colleagues are tiptoeing around but I think we’d better acknowledge it if we ever want to raise mathematic literacy.

Sweden is very welcoming to immigrants and almost everybody happily speaks English with me, often so well that I can’t tell if they’re native Swedes or Brits. At my workplace, the default language is English, both written and spoken. I have neither the exposure, nor the need, nor the use for Swedish. As a theoretical physicist, I have plenty of need for and exposure to math. But most people don’t.

“My STEM education colleagues like to point out that few adults would happily admit to not being able to read, but these same people have no trouble saying they’re bad at math.”

I like to point out it’s more surprising they like to point this out than this being the case. Life is extremely difficult when one can’t read neither manuals, nor bills, nor all the forms and documents that are sometimes mistaken for hallmarks of civilization. Not being able to read is such a disadvantage that it makes people wonder what’s wrong with you. But besides the basics that come in handy to decipher the fine print on your contracts, math is relevant only to specific professions.

I am lying of course when I say I was always bad with languages. I was bad with French and Latin and as my teachers told me often enough, that was sheer laziness. Je sais, tu sais, nous savons - Why make the effort? I never wanted to move to France. I learned English just fine: it was useful and I heard it frequently. And while my active Swedish vocabulary never proceeded beyond the very basics, I quickly learned Swedish to the extent that I need it. For all these insurance forms and other hallmarks of civilization, to read product labels, street signs and parking tickets (working on it).

I think that most people are also lying when they say they were always bad at math. They most likely weren’t bad, they were just lazy, never made an effort and got away with it, just as I did with my spotty Latin. The human brain is energetically highly efficient, but the downside is the inertia we feel when having to learn something new, the inertia that’s asking “Is it worth it? Wouldn’t I be better off hitting on that guy because he looks like he’ll be able to bring home food for a family?”

But mathematics isn’t the language of a Northern European country with a population less than that of other countries’ cities. Mathematics is the language of nature. You can move out of Sweden, but you can’t move out of the universe. And much like one can’t truly understand the culture of a nation without knowing the words at the basis of their literature and lyrics, one can’t truly understand the world without knowing mathematics.

Almost everybody uses some math intuitively. Elementary logic, statistics, and extrapolations are to some extent hardwired in our brains. Beyond that it takes some effort, yes. The reward for this effort is the ability to see the manifold ways in which natural phenomena are related, how complexity arises from simplicity, and the tempting beauty of unifying frameworks. It’s more than worth the effort.

One should make a distinction here between reading and speaking mathematics.

If you work in a profession that uses math productively or creatively, you need to speak math. But for the sake of understanding, being able to read math is sufficient. It’s the difference between knowing the meaning of a differential equation, and being able to derive and solve it. It’s the difference between understanding the relevance of a theorem, and leading the proof. I believe that the ability to ‘read’ math alone would enrich almost everybody’s life and it would also benefit scientific literacy generally.

So needless to say, I am supportive of attempts to raise interest in math. I am just reluctant to join complaints about the bad-at-math excuse because this discussion more often than not leaves aside that people aren’t interested because it’s not relevant to them. And that what is relevant to them most mathematicians wouldn’t even call math. Without addressing this point, we’ll never convince anybody to make the effort to decipher a differential equation.

But of course people learn all the time things they don’t need! They learn to dance Gangnam style, speak Sindarin, or memorize the cast of Harry Potter. They do this because the cultural context is present. Their knowledge is useful for social reasons. And that is why I think to raise mathematic literacy the most important points are:

Exposure

Popular science writing rarely if ever uses any math. I want to see the central equations and variables. It’s not only that metaphors and analogies inevitably have shortcomings, but more importantly it’s that the reader gets away with the idea that one doesn’t actually need all these complicated equations. It’s a slippery slope that leads to the question what we need all these physicists for anyway. The more often you see something, the more likely you are to think and talk about it. That’s why we’re flooded with frequently nonsensical adverts that communicate little more than a brand name, and that’s why just showing people the math would work towards mathematic literacy.

I would also really like to see more math in news items generally. If experts are discussing what they learned from the debris of a plane crash, I would be curious to hear what they did. Not in great detail, but just to get a general idea. I want to know how the number quoted for energy return on investment was calculated, and I want to know how they arrived at the projected carbon capture rate. I want to see a public discussion of the Stiglitz theorem. I want people to know just how often math plays a role for what shapes their life and the lives of those who will come after us.

Don’t tell me it’s too complicated and people won’t understand it and it’s too many technical terms and, yikes, it won’t sell. Look at the financial part of a newspaper. How many people really understand all the terms and details, all the graphs and stats? And does that prevent them from having passionate discussions about the stock market? No, it doesn’t. Because if you’ve seen and heard it sufficiently often, the new becomes familiar, and people talk about what they see.

Culture

We don’t talk about math enough. The residue theorem in complex analysis is one of my favorite theorems. But I’m far more likely to have a discussion about the greatest songs of the 60s than about the greatest theorems of the 19th century. (Sympathy for the devil.) The origin of this problem is lack of exposure, but even with the exposure people still need the social context to put their knowledge to use. So by all means, talk about math if you can and tell us what you’re sinking about!

Thursday, December 12, 2013

Massive gravity, a modification of general relativity in which gravitons have mass, has an interesting history. Massive gravity was long believed to be internally inconsistent, but physicists at Stockholm University now claim to have constructed a consistent theory for massive gravity. This theory is a viable alternative to general relativity and can address some of its problems.

In Einstein’s theory of general relativity gravitational waves spread with the speed of light, and the quanta of the gravitational field, the gravitons, are expected to do the same*. To be more precise, gravitons move with the speed of massless particles because they are assumed to be massless. But whether or not a particle is indeed massless is in the end a question of experiment.

Neutrinos were long believed to be massless, but we know today that at least two of them have tiny non-zero masses (whose absolute value has not yet been determined). The mass of the photon is known to be zero to extremely high precision on experimental grounds. But what about gravity? This is a timely question because a small mass would lead to a long-distance modification of general relativity, and present observational evidence left physicists with some puzzles at these long distances, notably dark energy and dark matter.

However, to be able to even properly ask whether gravitons have masses, we need a consistent theory for massive gravity. But making gravitons massive is a challenge for the theoretical physicist. In fact, it was long believed to be impossible.

The problems start when you want to introduce a mass-term into general relativity. For vector fields, you can take a contraction of fields of the form AνAν to stand in front of the mass term. In general relativity the field is the metric tensor, and the only full contractions that you can create without using derivatives are constant: they create a cosmological constant, not a graviton mass. If you want a mass-term in general relativity you need a second two-tensor, that is a field which looks like a metric but isn’t the metric. Theories of this type are also known as ‘bi-metric’. Massive gravity is thus intimately related to bi-metric gravity.

But that’s only the beginning of the problems, a beginning that dates back more than 70 years.

In 1939, Fierz and Pauli wrote down a theory of massive gravity in the perturbative limit. They found that for the theory to be consistent – meaning free of ‘ghosts’ that lead to unphysical instabilities – the parameters in the mass-terms must have specific values. With these values, the theory is viable.

In 1970 however, van Dam and Veltman and, independently, Zukharov, showed that in the Fierz-Pauli approach, the limit in which the mass of the graviton is taken to zero is not continuous and does, contrary to naïve expectations, not reproduce general relativity. Any graviton mass, regardless how small, leads to deviations that can contribute factors of order one to observables, which is in conflict with observation. The Fierz-Pauli theory now seemed theoretically fine, but experimentally ruled out.

Two years later, in 1972, Vainshtein argued that this discontinuity is due to the treatment of the gravitational degrees of freedom in the linearization procedure and can be cured in a full, non-linear, version of massive gravity. Unfortunately, in the same year, Deser and Boulware claimed that any non-linear completion of the Fierz-Pauli approach reintroduces the ghost. So now massive gravity was experimentally fine but theoretically sick.

Nothing much happened in this area for more than 30 years. Then, in the early 2000s, the wormy can was opened again by Arkani-Hamed et al and Creminelli et al, but they essentially confirmed the Deser-Boulware problem.

The situation began to look brighter in 2010, when de Rahm, Gabadadze and Tolley proposed a theory of massive gravity that did not suffer from the ghost-problem in a certain limit. Needless to say, after massive gravity had been thought dead and buried for 40 years, nobody really believed this would work. The de Rahm-Gabadadze approach did not make many friends because the second metric was treated as a fixed background field, and the theory was shown to allow for superluminal propagation (and, more recently, acausality).

However, starting in 2011, Fawad Hassan and Rachel Rosen from Stockholm University (ie next door), succeeded in formulating a theory of massive gravity that does not suffer from the ghost instability. The key to success was a generalization of the de Rahm-Gabadadze approach in which the second metric is also fully dynamic, and the interaction terms between the two metrics take on a specific form. The specific form of the interaction terms is chosen such that it generates a constraint which removes the ghost field. The resulting theory is to best present knowledge fully consistent and symmetric between the two metrics.

(Which, incidentally, explains my involvement with the subject, as I published a paper with a fully dynamic, symmetric, bi-metric theory in 2008, though I wasn’t interested in the massive case and don’t have interaction terms. The main result of my paper is that I ended up in defense committees of Fawad’s students.)

In the last years, the Stockholm group has produced a series of very interesting papers that not only formalizes their approach and shows its consistency, but they also derived specific solutions. This is not a small feat as it is already difficult to find solutions in general relativity if you have only one metric and having two doesn’t make the situation easier. Indeed, not many solutions are presently known, and the known ones have quite strong symmetry assumptions. (More students in the pipe...)

What is missing right now though is a smoking-gun signal, some observation that would allow to distinguish massive gravity from standard general relativity and could be used to distinguish between both. This is presently a very active area of research and one that I’m sure we’ll hear more about.

Saturday, December 07, 2013

During the last years a lot of attention has been drawn to the prevalence of irreproducible results in science. That published research findings tend to weaken or vanish over time is a pressing problem in particular in some areas of the life sciences, psychology and neuroscience. On the face of it, the issue is that scientists work with too small samples and frequently cherry-pick their data. Next to involuntarily poor statistics, the blame has primarily been put on the publish-or-perish culture of modern academia.

While I blame that culture for many ills, I think here the finger is pointed at the wrong target.

Scientists aren’t interested in publishing findings that they suspect to be spurious. That they do it anyway is because a) funding agencies don’t hand out sufficient money for decent studies with large samples b) funding agencies don’t like reproduction studies because, eh, it’s been done before and c) journals don’t like to publish negative findings. The latter in particular leads scientists to actively search for effects, which creates a clear bias. It also skews meta-studies against null results.

That’s bad, of course.

I will not pretend that physics is immune to this problem, though in physics the issue is, forgive my language, significantly less severe.

A point in case though is the application of many different analysis methods to the same data set. Collaborations have their procedures sorted out to avoid this pitfall, but once the data is public it can be analyzed by everybody and their methods, and sooner or later somebody will find something just by chance. That’s why, every once in while we hear of a supposedly interesting peculiarity in the cosmic microwave background, you know, evidence for a bubble collision, parallel universes, a cyclic universe, a lopsided universe, an alien message, and so on. One cannot even blame them for not accounting for other researchers who are trying creative analysis methods on the same data, because that’s unknown unknowns. And theoretical papers can be irreproducible in the sense of just being wrong, but the vast majority of these just get ignored (and if not the error is often of interest in itself).

So even while the fish at my doorstep isn’t the most rotten one, I think irreproducible results are highly problematic, and I welcome measures that have been taken, eg by Nature magazine, to improve the situation.

“There is a larger lesson to be gleaned from this brief history. If replication were the gold standard of scientific progress, we would still be banging our heads against our benches trying to arrive at the precise values that Galileo reported.”

You might forgive Jared, who is a is a PhD candidate in cognitive neuroscience, for cherry picking his historical data, because he’s been trained in today’s publish-and-perish culture. Unfortunately, he’s not the only one who believes that something is okay because a few people in the past succeeded with it. Michael Brooks has written a whole book about it. In “Free Radicals: The Secret Anarchy of Science”, you can read for example

“It is the intuitive understanding, the gut feeling about what the answer should be, that marks the greatest scientists. Whether they fudge their data or not is actually immaterial.”

Possibly the book gets better after this, but I haven’t progressed beyond this page because every time I see that paragraph I want to cry.

The “gut feeling about what the answer should be” does mark great scientists, yes. It also marks pseudoscientists and crackpots, just that you don’t find these the history books. The argument that fudging data is okay because great scientists did it and time proved them right is like browsing bibliographies and concluding that in the past everybody was famous.

I’m not a historian and I cannot set that record straight, but I can tell you that the conclusion that irreproducibility is a necessary ingredient to scientific progress is unwarranted.

But I have one piece of data to make my case, a transcript of a talk given by Irwin Langmuir in the 1950s, published in Physics Today in 1989. It carries the brilliant title “Pathological Science” and describes Langmuir’s first-hand encounters with scientists who had a gut feeling about what the answer should be. I really recommend you read the whole thing (pdf here), but just for the flavor here’s an excerpt:

“Mitogenic rays.
About 1923 there was a whole series of papers by Gurwitsch and others. There were hundreds of them published on mitogenic rays. There are still a few of them being published [in 1953]. I don’t know how many of you have ever heard of mitogenic rays. They are given off by growing plants, living things, and were proved, according to Gurwitsch, to be something that would go through glass but not through quarz. They seemed to be some sort of ultraviolet light… If you looked over these photographic plates that showed this ultraviolet light you found that the amount of light was not so much bigger than the natural particles of the photographic plate, so that people could have different opinions as to whether or not it showed this effect. The result was that less than half of the people who tried to repeat these experiments got any confirmation of it…”

Langmuir relates several stories of this type, all about scientists who discarded some of their data or read output to their favor. None of these scientists has left a mark in the history books. They have however done one thing. They’ve wasted their and other scientist’s time by not properly accounting for their methods.

There were hundreds of papers published on a spurious result – in 1953. Since then the scientific community has considerably grown, technology has become much more sophisticated (not to mention expensive), and scientists have become increasingly specialized. For most research findings, there are very few scientists who are able to conduct a reproduction study, even leaving aside the problems with funding and publishing. In 2013, scientists have to rely on their colleagues much more than was the case 60 years ago, and certainly in the days of Millikan and Galileo. The harm being caused by cherry picked data and non-reported ‘post-selection’ (a euphemism for cherry-picking), in terms of waste of time has increase with the community. Heck, there were dozens of researchers who wasted time (and thus their employers money...) on ‘superluminal neutrinos’ even though everybody knew these results to be irreproducible (in the sense that they hadn’t been found by any previous measurements).

Worse, this fallacious argument signals a basic misunderstanding about how science works.

The argument is based on the premise that if a scientific finding is correct, it doesn’t matter where it came from or how it was found. That is then taken to justify the ignorance of any scientific method (and frequently attributed to Feyerabend). It is correct in that in the end it doesn’t matter exactly how a truth about nature was revealed. But we do not speak of a scientific method to say that there is only one way to make progress. The scientific method is used to increase the chances of progress. It’s the difference between letting the proverbial monkey hammer away and hiring a professional science writer for your magazine’s blog. Yes, the monkey can produce a decent blogpost, and if that is so then that is so. But chances are eternal inflation will end before you get to see a good result. That’s why scientists have quality control and publishing ethics, why we have peer review and letters of recommendation, why we speak about statistical significance and double-blind studies and reproducible results: Not because in the absence of methods nothing good can happen, but because these methods have proven useful to prevent us from fooling ourselves and thereby make success considerably more likely.

Having said that, expert intuition can be extremely useful and there is nothing wrong with voicing a “gut feeling” as long as it is marked as such. It is unfortunate indeed that the present academic system does not give much space for scientists to express their intuition, or maybe they are shying away from it. But that’s a different story and shell be told another time.

So the answer to the question posed in the title is a clear no. The question is not whether science has progressed despite the dishonest methods that have been employed in the past, but how much better if would have progressed if that had not been so.

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I stole that awesome gif from over here. I don't know its original source.

Wednesday, December 04, 2013

If life grows over your head, your closest pop psy magazine recommends dividing it up into small, manageable chunks. Physicists too apply this method in difficult situations. Discrete approximations – taking a system apart into chunks – are enormously useful to understand emergent properties and to control misbehavior, such as divergences. Discretization is the basis of numerical simulations, but can also be used in an analytic approach, when the size of chunks is eventually taken towards zero.

Understanding space and time in the early universe is such a difficult situation where gravity is misbehaved and quantum effects of gravity should become important, yet we don’t know how to deal with them. Discretizing the system and treating it similar to other quantum systems is the maybe most conservative approach one can think of, yet it is challenging. Normally, discretization is used for a system within space and time. Now it is space and time themselves that are being discretized. There is no underlying geometry as reference on which to discretize.

Causal Dynamical Triangulations (CDT), pioneered by Loll, Ambjørn and Jurkiewicz, realizes this most conservative approach towards quantum gravity. Geometry is decomposed into triangular chunks (or their higher-dimensional versions respectively) and all possible geometries are summed over in a path integral (after Wick-rotation) with the weight given by the discretized curvature. The curvature is encoded in the way the chunks are connected to each other. The term ‘causal’ refers to a selection principle for geometries that are being summed over. In the end, the continuum limit can be taken, so this approach in an by itself doesn’t mean that spacetime fundamentally is discrete, just that it can be approximated by a discretization procedure.

The path integral that plays the central role here is Feynman’s famous brain child in which a quantum system takes all possible paths, and observables are computed by suitably summing up all possible contributions. It is the mathematical formulation of the statement that the electron goes through both slits. In CDT it’s space-time that goes through all allowed chunk configurations.

Evaluating the path integral of the triangulations is computationally highly intensive, but simple universes can now be simulated numerically. The results that have been found during the last years are promising: The approach produces a smooth extended geometry that appears well-behaved. This doesn’t sound like much, but keep in mind that they didn’t start with anything resembling geometry! It’s discrete things glued together, but it reproduces a universe with a well-behaved geometry like the one we see around.

Or does it?

The path integral of CDT contains free parameters, and most recently the simulations found that the properties of the universe it describes depend on the value of the parameters. I find this very intriguing because it means that, if space-time's quantum properties are captured by CDT, then space-time has various different phases, much like water has different phases.

The parameter κ is proportional to the inverse of Newton’s constant, and the parameter Δ quantifies the (difference in the) abundance of two different types of chunks that space-time is built up of. The phase marked C in the upper left, with the Hubble image, is where one finds a geometry resembling our universe. In the phase marked A to the right space-time falls apart into causally disconnected pieces. In the phase marked B at the bottom, space-time clumps together into a highly connected graph with a small diameter that doesn’t resemble any geometry. The numerical simulations indicate that the transition between the phases C and A is first order, and between C and B it’s second order.

In summary, in phase A everything is disconnected. In phase B everything is connected. In phase C you can share images of your lunch with people you don’t know on facebook.

Now you might say, well, but the parameters are what they are and facebook is what it is. But in quantum theory, parameters tend to depend on the scale, that is the distance or energies by which a system is probed. Physicists say “constant’s run”, which just rephrases the somewhat embarrassing statement that a constant is not constant. Since our universe is not in thermal equilibrium and has cooled down from a state of high temperature, constants have been running, and our universe can thus have passed through various phases in parameter space.

Of course it might be that CDT in the end is not the right way to describe the quantum properties of gravity. But I find this a very interesting development, because such a geometric phase transition might have left observable traces and brings us one step closer to experimental evidence for quantum gravity.

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You can find a very good brief summary of CDT here, and the details eg in this paper.

Images used in the background of the phase-diagram, are from here, here and here.